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[2602.14478] Constrained and Composite Sampling via Proximal Sampler
Summary
This paper presents a novel approach to constrained and composite sampling using a proximal sampler, addressing challenges in enforcing feasibility while maintaining mixing efficiency.
Why It Matters
The findings are significant for machine learning and optimization, particularly in Bayesian inference, as they introduce a practical method for sampling from complex distributions with minimal oracle access, enhancing computational efficiency and applicability in real-world scenarios.
Key Takeaways
- Introduces a proximal sampler for constrained sampling that requires minimal oracle access.
- Demonstrates a novel approach to composite sampling by reducing it to constrained sampling.
- Establishes mixing time bounds using Rényi and χ² divergences, contributing to theoretical understanding.
- Addresses practical challenges in sampling from log-concave distributions.
- Enhances Bayesian inference methods by separating data fidelity and prior information.
Statistics > Machine Learning arXiv:2602.14478 (stat) [Submitted on 16 Feb 2026] Title:Constrained and Composite Sampling via Proximal Sampler Authors:Thanh Dang, Jiaming Liang View a PDF of the paper titled Constrained and Composite Sampling via Proximal Sampler, by Thanh Dang and 1 other authors View PDF HTML (experimental) Abstract:We study two log-concave sampling problems: constrained sampling and composite sampling. First, we consider sampling from a target distribution with density proportional to $\exp(-f(x))$ supported on a convex set $K \subset \mathbb{R}^d$, where $f$ is convex. The main challenge is enforcing feasibility without degrading mixing. Using an epigraph transformation, we reduce this task to sampling from a nearly uniform distribution over a lifted convex set in $\mathbb{R}^{d+1}$. We then solve the lifted problem using a proximal sampler. Assuming only a separation oracle for $K$ and a subgradient oracle for $f$, we develop an implementation of the proximal sampler based on the cutting-plane method and rejection sampling. Unlike existing constrained samplers that rely on projection, reflection, barrier functions, or mirror maps, our approach enforces feasibility using only minimal oracle access, resulting in a practical and unbiased sampler without knowing the geometry of the constraint set. Second, we study composite sampling, where the target is proportional to $\exp(-f(x)-h(x))$ with closed and convex $f$ and $h$. This composite structure is stan...
